Question

How do you combine `(x+2)/(5x^2)+(x+4)/(15x)`?

Answer 1

`[x^2 + 7x+ 6]/(15x^2)`

Explanation:

Adding fractions requires a common denominator.

The LCD is `15x^2`

An equivalent fraction for each fraction must be found with the denominator `15x^2`

`color(magenta)[(x+2)/(5x^2])+color(blue)[(x+4)/(15x)]`

`color(magenta)[(x+2)/(5x^2) xx 3/3 = (3(x+2))/(15x^2])`

`color(blue)[(x+4)/(15x) xx x/x = (x(x+4))/(15x^2)]`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(magenta)[(x+2)/(5x^2])+color(blue)[(x+4)/(15x)]`

=`color(magenta)[(3(x+2))/(15x^2)] + color(blue)[(x(x+4))/(15x^2) ]`

= `[color(magenta)(3x+6) + color(blue)(x^2+4x])/(15x^2)`

= `[x^2 + 7x+ 6]/(15x^2)`